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Properties

Label 1584.2.dp
Level $1584$
Weight $2$
Character orbit 1584.dp
Rep. character $\chi_{1584}(29,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $4544$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.dp (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1584 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

Total New Old
Modular forms 4672 4672 0
Cusp forms 4544 4544 0
Eisenstein series 128 128 0

Trace form

\( 4544 q - 30 q^{2} - 12 q^{3} - 6 q^{4} - 18 q^{5} - 20 q^{6} + O(q^{10}) \) \( 4544 q - 30 q^{2} - 12 q^{3} - 6 q^{4} - 18 q^{5} - 20 q^{6} - 24 q^{11} - 32 q^{12} - 10 q^{13} - 18 q^{14} - 24 q^{15} - 6 q^{16} - 20 q^{18} - 40 q^{19} - 18 q^{20} - 8 q^{22} - 20 q^{24} - 12 q^{27} - 40 q^{28} - 30 q^{29} - 20 q^{30} - 12 q^{31} - 32 q^{33} - 8 q^{34} + 4 q^{36} - 24 q^{37} - 18 q^{38} - 10 q^{40} - 56 q^{42} - 52 q^{45} - 36 q^{47} + 8 q^{48} + 508 q^{49} - 30 q^{50} - 20 q^{51} - 10 q^{52} - 132 q^{56} - 6 q^{58} - 18 q^{59} - 112 q^{60} - 10 q^{61} - 40 q^{63} - 24 q^{64} + 8 q^{66} - 16 q^{67} - 420 q^{68} + 6 q^{69} - 48 q^{70} + 130 q^{72} - 30 q^{74} + 20 q^{75} - 24 q^{77} - 128 q^{78} - 20 q^{79} - 24 q^{81} - 8 q^{82} - 30 q^{83} - 90 q^{84} - 10 q^{85} - 18 q^{86} + 88 q^{88} - 200 q^{90} - 80 q^{91} - 246 q^{92} - 24 q^{93} - 10 q^{94} - 60 q^{95} - 20 q^{96} - 12 q^{97} - 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.